# Surface Area of Sphere

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## Theorem

The surface area $A$ of a sphere whose radius $a$ is given by:

- $A = 4 \pi a^2$

## Proof

## Historical Note

The Surface Area of Sphere was demonstrated by Archimedes

His proof appears as Proposition $34$ in his *On the Sphere and Cylinder*.

He also discusses this result in his *The Method*:

*From this theorem, to the effect that a sphere is four times as great as the cone with a great circle of the sphere as base and height equal to the radius of the sphere, I conceived the notion that the surface of any sphere is four times as great as a great circle in it; for, judging from the fact that any circle is equal to a triangle with base equal to the circumference and height equal to the radius of the circle, I apprehended that, in like manner, a sphere is equal to a cone with base equal to the surface of the sphere and height equal to the radius.*

## Sources

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**sphere** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**sphere**